Instability of stratified two-phase flows in inclined rectangular ducts

The effect of inclination on instability of two-phase stratified flow in inclined rectangular ducts is studied for the first time via a rigorous linear stability analysis that accounts for all possible infinitesimal three-dimensional disturbances. The results of stability analysis of concurrent downward, concurrent upward, and countercurrent air-water flows are presented in the form of stability diagrams in the coordinates of critical superficial velocities for each of the cases at a characteristic set of other governing parameters. The multiplicity of base-flow solutions predicted for inclined flows is addressed. This study is the first to show that within the rigorous formulation of the stability problem in a realistic duct geometry, the concurrent upward two-phase flows allow for multiple stable flow states. While the main bulk of results is obtained for ducts with a square cross-section, the effect of the duct aspect ratio on the onset of instability is studied for several representative examples. It is shown that in most cases the flow becomes unstable due to different modes of long-wave disturbances that are associated with either interface or shear instability mechanisms. The latter arises mainly due to the duct bottom and top walls. The results substantiate the premise that the simpler two-plate geometry can be used to estimate the effect of the system parameters on the flow stability. The three-dimensional finite-wavelength critical disturbances are visualized by a novel approach of divergence-free projections on the coordinate planes.